The rho cube : some results, some problems

Horatiu Cirstea 1 Claude Kirchner 1 Luigi Liquori 2, 3 Benjamin Wack 1, 3
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 MIRHO - Objects, types and prototypes : semantics and validation
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7503
Abstract : The rewriting calculus embeds in a same setting the lambda calculus and the rewriting, by allowing abstraction not only on variables but also on patterns. The higher-order mechanisms of the lambda-calculus and the pattern matching facilities of the rewriting are then both available at the same level. It is worth noticing that the complexity of the calculu breaks the confluence property, so that we need to define appropiate strategies or restrictions, in order to recover it. We choose here to look at the rho-calculus as an extension of the lambda-calculus, and we study the typed aspects. Our study is based upon a generalization of Barendregt's lambda-cube, in which we unify both abstractors lambda and Pi into a single one. We need to deal with the original features of the rho-calculus too: matching power, non-determinism, confluence issues. With proper restrictions, we have proved most of the usual properties for typed calculi: substitution lemma, correctness of types, subject reduction, consistency. Uniqueness of typing is generally no longer valid but we can still prove it for one of the most restrictive systems, rho-> and rho2.
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Submitted on : Tuesday, September 26, 2006 - 9:01:59 AM
Last modification on : Saturday, January 27, 2018 - 1:31:35 AM
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Horatiu Cirstea, Claude Kirchner, Luigi Liquori, Benjamin Wack. The rho cube : some results, some problems. First International Workshop on Higher-Order Rewriting Copenhagen, Denmark, July 21st, 2002 Affiliated with RTA 2002, D. Kesner, T. Nipkow and F. van Raamsdonk, Jul 2002, Copenhague, Denmark. ⟨inria-00099411⟩

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